Logical Reasoning - Logical Deduction
In each of the following questions, three statements are given followed by four conclusions numbered I, II, III and TV. You have to take the given statements to be true even if they seem to be at variance with commonly known facts and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.
Statements: All buildings are windows. No toys is building. Some tigers are toys.
Conclusions:
- Some tigers are buildings.
- Some windows are tigers.
- All toys are tigers.
- Some windows are toys.
No toy is building. All buildings are windows.
Since the middle term 'buildings' is distributed twice and one premise is negative, the conclusion must be particular negative and should not contain the middle term.
So, it follows that 'Some windows are not toys'.
Some tigers are toys. No toy is building.
Since one premise is particular and the other premise is negative, the conclusion must be particular negative and should not contain the middle term. So, it follows that 'Some tigers are not buildings'.
Statements: Some papers are cats. All cats are bats. No bat is horse.
Conclusions:
- Some papers are horses.
- No horse is cat.
- Some bats are papers.
- All papers are bats.
Some papers are cats. All cats are bats.
Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some papers are bats'. III is the converse of this conclusion and so it holds.
All cats are bats. No bat is horse.
Since both the premises are universal and one premise is negative, the conclusion must be universal negative and should not contain the middle term. So, it follows that 'No cat is horse'. II is the converse of this conclusion and so it holds.
Some papers are bats. No bat is horse.
Since one premise is particular and the other negative, the conclusion must be particular negative and should not contain the middle term. So, it follows that 'Some papers are not horses'.
Statements: Some tapes are discs. Some discs are cassettes. Some cassettes are songs.
Conclusions:
- Some songs are discs.
- Some cassettes are tapes.
- Some songs are tapes.
- No song is a disc.
Since each combination of premises shall contain two particular premises, no definite conclusion can be drawn. However, I and IV involve the extreme terms of the second and third premises and form a complementary pair. Thus, either I or IV follows.
Statements: No table is fruit. No fruit is window. All windows are chairs.
Conclusions:
- No window is table.
- No chair is fruit.
- No chair is table.
- All chairs are windows.
No table is fruit. No fruit is window.
Since both the premises are negative, no definite conclusion follows.
No fruit is window. All windows are chairs.
Since the middle term 'windows' is distributed twice and one premise is negative, the conclusion must be particular negative. So, it follows that 'Some chairs are not fruits'.
Statements: All jungles are buses. All books are buses. All fruits are books.
Conclusions:
- Some fruits are jungles.
- Some buses are books.
- Some buses are jungles.
- All fruits are buses.
III is the converse of the first premise and II is the converse of the second premise.
So, both of them hold.
All fruits are books. All books are buses.
Since both the premises are universal and affirmative, the conclusion must be universal affirmative and should not contain the middle term. So, it follows that 'All fruits are buses'. Thus, IV follows.
All jungles are buses. All books are buses.
Since the middle term 'buses' is not distributed ever once in the premises, no definite conclusion follows.
All fruits are buses. All books are buses.
As discussed above, no definite conclusion can be drawn.
All jungles are buses. All fruits are buses.
Again, no definite conclusion follows.